A new diagnostic test for tuberculosis has sensitivity 85% and specificity 90%. In a district with TB prevalence of 20%, what is the Positive Predictive Value (PPV) of this test?
- A 52.9%
- B 73.4%
- C 68.0% ✓
- D 81.0%
Correct answer: C. 68.0%
Explanation
TP = 0.85 × 200 = 170; FP = 0.10 × 800 = 80 (using a population of 1000 with 200 TB cases and 800 non-cases). PPV = 170 / (170 + 80) = 170/250 = 0.68 = 68%. NPV = TN/(TN+FN) = 720/(720+30) = 96%. PPV depends heavily on prevalence: the same test in a 5% prevalence population would have PPV = (0.85×50)/((0.85×50)+(0.10×950)) = 42.5/137.5 = 30.9%, illustrating why population prevalence must be considered when interpreting PPV.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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